Topic
Alpha beta filter
About: Alpha beta filter is a research topic. Over the lifetime, 5653 publications have been published within this topic receiving 128415 citations.
Papers published on a yearly basis
Papers
More filters
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TL;DR: In this paper, the problem of designing an observer to estimate a linear function of the state of a linear system, for the purpose of implementing a feedback control law is considered, and a procedure for constructing the observer and an algorithm for determining minimal order is outlined.
Abstract: This paper considers the problem of designing an observer to estimate a linear function of the state of a linear system, for the purpose of implementing a feedback control law. In the single-output case a necessary and sufficient condition is found for the existence of an observer of given order and pole configuration. A procedure is stated for constructing the observer, and an algorithm for determining minimal order is outlined. The multi-output case is reduced via a canonical form to an output-coupled set of single-output systems which can be treated as above. Observers derived using these procedures are generally of lower order than those of Luenberger, and the restriction that plant and observer have no common poles is unnecessary.
184 citations
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TL;DR: In this paper, a new nonlinear filter for continuous-time processes with discrete-time measurements is proposed, which is exact and can be implemented in real time with a computational complexity comparable to the Kalman filter.
Abstract: A new nonlinear filter is derived for continuous-time processes with discrete-time measurements. The filter is exact, and it can be implemented in real time with a computational complexity that is comparable to the Kalman filter. This new filter includes both the Kalman filter and the discrete-time version of the Benes filter as special cases. Moreover, the new theory can handle a large class of nonlinear estimation problems that cannot be solved using the Kalman or discrete-time Benes filters. A simple approximation technique is suggested for practical applications in which the dynamics do not satisfy the required conditions exactly. This approximation is analogous to the so-called "extended Kalman filter" [10], and it represents a generalization of the standard linearization method.
181 citations
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TL;DR: In this paper, a multivariate-t-based Kalman filter model is proposed, where the posterior distribution will revert to the prior when extreme outlying observations are encountered, and this can be achieved by assuming a multiivariate distribution with Student-t marginals.
Abstract: Kalman filter models based on the assumption of multivariate Gaussian distributions are known to be nonrobust. This means that when a large discrepancy arises between the prior distribution and the observed data, the posterior distribution becomes an unrealistic compromise between the two. In this article we discuss a rationale for how to robustify the Kalman filter. Specifically, we develop a model wherein the posterior distribution will revert to the prior when extreme outlying observations are encountered, and we point out that this can be achieved by assuming a multivariate distribution with Student-t marginals. To achieve fully robust results of the kind desired, it becomes necessary to forsake an exact distribution-theory approach and adopt an approximation method involving “poly-t” distributions. A recursive mechanism for implementing the multivariate-t—based Kalman filter is described, its properties are discussed, and the procedure is illustrated by an example.
178 citations
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TL;DR: For non-linear MIMO systems, the extended Luenberger observer as discussed by the authors is a nonlinear observer design for all sufficiently smooth and locally observable systems that can be simplified using the degrees of freedom available in the case of multiple outputs.
Abstract: For non-linear multiple-input multiple-output systems [xdot] = f(x, u), y = h(x, u), nonlinear observers are designed using a transformation into the non-linear observer canonical form and an extended linearization The differential equation of observer error in canonical coordinates is linearized about the reconstructed trajectory, and dimensioned by eigenvalue assignment With reference to the extended Kalman filter algorithm, this non-linear observer design is called the extended Luenberger observer This observer design is possible for all sufficiently smooth and locally observable systems In comparison with single-output systems, the non-linear observer design can be essentially simplified using the degrees of freedom available in the case of multiple outputs
177 citations
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22 May 2003TL;DR: Novel algorithms for predictive tracking of user position and orientation based on double exponential smoothing are presented, which are faster, easier to implement, and perform equivalently to the Kalman and extended Kalman filtering predictors.
Abstract: We present novel algorithms for predictive tracking of user position and orientation based on double exponential smoothing. These algorithms, when compared against Kalman and extended Kalman filter-based predictors with derivative free measurement models, run approximately 135 times faster with equivalent prediction performance and simpler implementations. This paper describes these algorithms in detail along with the Kalman and extended Kalman Filter predictors tested against. In addition, we describe the details of a predictor experiment and present empirical results supporting the validity of our claims that these predictors are faster, easier to implement, and perform equivalently to the Kalman and extended Kalman filtering predictors.
176 citations